Characteristic map of Catmull-Clark subdivision

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Equations

Catmull-Clark characteristic map labeling
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Catmull-Clark characteristic map labeling
n := \mbox{valence}, \quad c := \cos{2\pi \over n}, \quad s := \sin{2\pi \over n}, \quad \lambda := { c + 5 + \sqrt{(c + 9) (c + 1)} \over 16 }
x = {4\lambda-1 \over 13020 } \left[ \begin{matrix} 0 \\ 4\lambda^2(64\lambda-1)(32\lambda-1)(16\lambda-1)(4\lambda-1) \\ 8\lambda^2(64\lambda-1)(32\lambda-1)(16\lambda-1) \\ 4\lambda^2(64\lambda-1)(928\lambda^2+228\lambda-31) \\ 8\lambda^2(64\lambda-1)(16\lambda-1)(4\lambda-1)(4\lambda+13) \\ 4\lambda^2(64\lambda-1)(928\lambda^2+228\lambda-31) \\ 80\lambda^2(1280\lambda^3+2128\lambda^2-56\lambda-13) \\ (64\lambda-1)(16\lambda-1)(4\lambda-1)(100\lambda^2+42\lambda-1) \\ 4\lambda(64\lambda-1)(640\lambda^3+688\lambda^2-82\lambda-1) \\ 20\lambda(2048\lambda^4+11040\lambda^3+812\lambda^2-165\lambda-1) \\ 40\lambda(5248\lambda^3+1568\lambda^2-133\lambda-5) \\ 20\lambda(2048\lambda^4+11040\lambda^3+812\lambda^2-165\lambda-1) \\ 4\lambda(64\lambda-1)(640\lambda^3+688\lambda^2-82\lambda-1) \\ \end{matrix} \right]
y = { s\lambda(64\lambda-1) \over 6510 } \left[ \begin{matrix} 0 \\ -4\lambda^2(32\lambda-1)(16\lambda-1) \\ 0 \\ 140\lambda^2(8\lambda-1) \\ -8\lambda^2(16\lambda-1)(4\lambda+13) \\ -140\lambda^2(8\lambda-1) \\ 0 \\ -(16\lambda-1)(100\lambda^2+42\lambda-1) \\ -4\lambda(160\lambda^2+132\lambda-1) \\ -20\lambda(8\lambda^2+15\lambda+1) \\ 0 \\ 20\lambda(8\lambda^2+15\lambda+1) \\ 4\lambda(160\lambda^2+132\lambda-1) \\ \end{matrix} \right]
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Latex code 

begin{align}
    n := \mbox{valence}, \quad
    c := \cos{2\pi \over n}, \quad
    s := \sin{2\pi \over n}, \quad
    \lambda := { c + 5 + \sqrt{(c + 9)  (c + 1)} \over 16 }
end{align}
begin{align}
    x =
    {4\lambda-1 \over 13020 }
    \left[
    \begin{matrix}
       0                                                                 \\
       4\lambda^2(64\lambda-1)(32\lambda-1)(16\lambda-1)(4\lambda-1)     \\
       8\lambda^2(64\lambda-1)(32\lambda-1)(16\lambda-1)                 \\
       4\lambda^2(64\lambda-1)(928\lambda^2+228\lambda-31)               \\
       8\lambda^2(64\lambda-1)(16\lambda-1)(4\lambda-1)(4\lambda+13)     \\
       4\lambda^2(64\lambda-1)(928\lambda^2+228\lambda-31)               \\
       80\lambda^2(1280\lambda^3+2128\lambda^2-56\lambda-13)             \\
       (64\lambda-1)(16\lambda-1)(4\lambda-1)(100\lambda^2+42\lambda-1)  \\
       4\lambda(64\lambda-1)(640\lambda^3+688\lambda^2-82\lambda-1)      \\
       20\lambda(2048\lambda^4+11040\lambda^3+812\lambda^2-165\lambda-1) \\
       40\lambda(5248\lambda^3+1568\lambda^2-133\lambda-5)               \\
       20\lambda(2048\lambda^4+11040\lambda^3+812\lambda^2-165\lambda-1) \\
       4\lambda(64\lambda-1)(640\lambda^3+688\lambda^2-82\lambda-1)      \\
    \end{matrix}
    \right]
end{align}
begin{align}
    y =
    { s\lambda(64\lambda-1) \over 6510 }
    \left[
    \begin{matrix}
        0                                        \\
        -4\lambda^2(32\lambda-1)(16\lambda-1)    \\
        0                                        \\
        140\lambda^2(8\lambda-1)                 \\
        -8\lambda^2(16\lambda-1)(4\lambda+13)    \\
        -140\lambda^2(8\lambda-1)                \\
        0                                        \\
        -(16\lambda-1)(100\lambda^2+42\lambda-1) \\
        -4\lambda(160\lambda^2+132\lambda-1)     \\
        -20\lambda(8\lambda^2+15\lambda+1)       \\
        0                                        \\
        20\lambda(8\lambda^2+15\lambda+1)        \\
        4\lambda(160\lambda^2+132\lambda-1)      \\
    \end{matrix}
    \right]
end{align}
Retrieved from "http://www.cise.ufl.edu/research/SurfLab/wiki/index.php?title=Characteristic_map_of_Catmull-Clark_subdivision"
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